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A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem

Author

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  • John W. Mamer

    (Anderson Graduate School of Management, University of California, Los Angeles, Box 951481, 110 Westwood Plaza, Los Angeles, California 90095-1481)

  • Richard D. McBride

    (Marshall School of Business, University of Southern California, Los Angeles, California 90089-0809)

Abstract

We propose and test a new pricing procedure for solving large-scale structured linear programs. The procedure interactively solves a relaxed subproblem to identify potential entering basic columns. The subproblem is chosen to exploit special structure, rendering it easy to solve. The effect of the procedure is the reduction of the number of pivots needed to solve the problem. Our approach is motivated by the column-generation approach of Dantzig-Wolfe decomposition. We test our procedure on two sets of multicommodity flow problems. One group of test problems arises in routing telecommunications traffic and the second group is a set of logistics problem which have been widely used to test multicommodity flow algorithms.

Suggested Citation

  • John W. Mamer & Richard D. McBride, 2000. "A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem," Management Science, INFORMS, vol. 46(5), pages 693-709, May.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:5:p:693-709
    DOI: 10.1287/mnsc.46.5.693.12042
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    References listed on IDEAS

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    Cited by:

    1. Richard D. McBride & John W. Mamer, 2004. "Implementing an LU Factorization for the Embedded Network Simplex Algorithm," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 109-119, May.
    2. F. Babonneau & O. du Merle & J.-P. Vial, 2006. "Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM," Operations Research, INFORMS, vol. 54(1), pages 184-197, February.
    3. P. Chardaire & G. P. McKeown & S. A. Verity-Harrison & S. B. Richardson, 2005. "Solving a Time-Space Network Formulation for the Convoy Movement Problem," Operations Research, INFORMS, vol. 53(2), pages 219-230, April.
    4. Mohammad Ali Raayatpanah & Salman Khodayifar & Thomas Weise & Panos Pardalos, 2022. "A novel approach to subgraph selection with multiple weights on arcs," Journal of Combinatorial Optimization, Springer, vol. 44(1), pages 242-268, August.
    5. Marco E. Lübbecke & Jacques Desrosiers, 2005. "Selected Topics in Column Generation," Operations Research, INFORMS, vol. 53(6), pages 1007-1023, December.
    6. Dipesh J. Patel & Rajan Batta & Rakesh Nagi, 2005. "Clustering Sensors in Wireless Ad Hoc Networks Operating in a Threat Environment," Operations Research, INFORMS, vol. 53(3), pages 432-442, June.
    7. Jean Bertrand Gauthier & Jacques Desrosiers & Marco E. Lübbecke, 2016. "Tools for primal degenerate linear programs: IPS, DCA, and PE," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(2), pages 161-204, June.
    8. Hatem Ben Amor & Jacques Desrosiers & José Manuel Valério de Carvalho, 2006. "Dual-Optimal Inequalities for Stabilized Column Generation," Operations Research, INFORMS, vol. 54(3), pages 454-463, June.
    9. Muter, İbrahim & Sezer, Zeynep, 2018. "Algorithms for the one-dimensional two-stage cutting stock problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 20-32.
    10. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    11. Garg, Manish & Smith, J. Cole, 2008. "Models and algorithms for the design of survivable multicommodity flow networks with general failure scenarios," Omega, Elsevier, vol. 36(6), pages 1057-1071, December.
    12. Christina N. Burt & Lou Caccetta, 2014. "Equipment Selection for Surface Mining: A Review," Interfaces, INFORMS, vol. 44(2), pages 143-162, April.
    13. ÇalIskan, Cenk, 2011. "A specialized network simplex algorithm for the constrained maximum flow problem," European Journal of Operational Research, Elsevier, vol. 210(2), pages 137-147, April.

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